Two classes of rank tests are considered for ordered alternatives in a randomized block design with $k$ treatments and $n$ blocks: tests based on among-blocks rankings ($A$-tests) and tests based on within-blocks rankings ($W$-tests). Previous efficiency comparisons for fixed $k, n \rightarrow \infty$ under the normal distribution have indicated that $A$-tests are more sensitive. In the present paper it is shown that this behavior is not typical under other distributions. Further, analysis of efficiencies for fixed $n, k \rightarrow \infty$ indicates greater sensitivity for $W$-tests. Considering these results and certain other desirable properties of the $W$-tests, the latter are recommended for most applications.
@article{1176342673,
author = {Pirie, Walter R.},
title = {Comparing Rank Tests for Ordered Alternatives in Randomized Blocks},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 374-382},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342673}
}
Pirie, Walter R. Comparing Rank Tests for Ordered Alternatives in Randomized Blocks. Ann. Statist., Tome 2 (1974) no. 1, pp. 374-382. http://gdmltest.u-ga.fr/item/1176342673/